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We study tail behaviour of the distributions of $W_n$ and $W$ in the case where $Z_1$ has heavy-tailed distribution, that is, $\\E e^{\\lambda Z_1}=\\infty$ for every $\\lambda>0$. We show how different types of distributions of $Z_1$ lead to different asymptotic behaviour of the tail of $W_n$ and $W$. 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